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Question Number 123075 by nico last updated on 22/Nov/20

Answered by Olaf last updated on 23/Nov/20

$$\frac{2n+2i+1}{2{(n+i)}^2}=\frac{1}{n+i}+\frac{1}{2{(n+i)}^2}$$$$\underset{i=1}{\sum ^n}\frac{1}{n+i}=\psi (2n+1)-\psi (n+1)$$$$\underset{i=1}{\sum ^n}\frac{1}{{(n+i)}^2}=\frac{1}{2}[-{\psi }_1(2n+1)+{\psi }_1(n+1)]$$$$tobecontinued...$$

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